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A348111
Numbers k whose binary expansion starts with the concatenation of the binary expansions of the run lengths in binary expansion of k.
1
0, 1, 7, 14, 28, 112, 127, 254, 509, 1016, 1018, 1792, 2033, 2037, 2039, 4066, 4072, 4075, 4078, 8132, 8135, 8150, 8156, 16256, 16300, 16313, 32513, 32528, 32576, 32601, 32607, 32626, 32639, 32767, 65027, 65087, 65153, 65202, 65248, 65253, 65255, 65534, 130307
OFFSET
1,3
COMMENTS
We consider here that 0 has an empty binary expansion, and include it in the sequence.
This sequence is infinite as it contains A077585.
LINKS
EXAMPLE
Regarding 32607:
- the binary expansion of 32607 is "111111101011111",
- the corresponding run lengths are: 7, 1, 1, 1, 5,
- in binary: "111", "1", "1", "1", "101",
- after concatenation: "111111101",
- as "111111101011111" starts with "111111101", 32607 belongs to this sequence.
PROG
(PARI) See Links section.
(Python)
from itertools import groupby
def ok(n):
if n == 0: return True
b = bin(n)[2:]
c = "".join(bin(len(list(g)))[2:] for k, g in groupby(b))
return b.startswith(c)
print(list(filter(ok, range(2**17)))) # Michael S. Branicky, Oct 02 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 01 2021
STATUS
approved